Continuous deformations of harmonic maps and their unitons

Alexandru Aleman, María J. Martín*, Anna Maria Persson, Martin Svensson

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

It is known that any harmonic map of finite uniton number from a Riemann surface into U (n) can be deformed into a new harmonic map with an associated S1-invariant extended solution. We study this deformation in detail using operator-theoretic methods. In particular, we show that the corresponding unitons are real analytic functions of the deformation parameter, and that the deformation is closely related to the Bruhat decomposition of the corresponding extended solution.

Original languageEnglish
JournalMonatshefte fur Mathematik
Volume190
Issue number4
Pages (from-to)599-614
Number of pages16
ISSN0026-9255
DOIs
Publication statusPublished - 1. Dec 2019

Fingerprint

Harmonic Maps
Bruhat Decomposition
Real Analytic Functions
Riemann Surface
Invariant
Operator

Keywords

  • Blaschke–Potapov products
  • Bruhat decomposition
  • Extended solutions
  • Harmonic maps
  • Shift-invariant subspaces
  • Unitons

Cite this

Aleman, Alexandru ; Martín, María J. ; Persson, Anna Maria ; Svensson, Martin. / Continuous deformations of harmonic maps and their unitons. In: Monatshefte fur Mathematik. 2019 ; Vol. 190, No. 4. pp. 599-614.
@article{3b3a05476db649008234d93e2e94eb42,
title = "Continuous deformations of harmonic maps and their unitons",
abstract = "It is known that any harmonic map of finite uniton number from a Riemann surface into U (n) can be deformed into a new harmonic map with an associated S1-invariant extended solution. We study this deformation in detail using operator-theoretic methods. In particular, we show that the corresponding unitons are real analytic functions of the deformation parameter, and that the deformation is closely related to the Bruhat decomposition of the corresponding extended solution.",
keywords = "Blaschke–Potapov products, Bruhat decomposition, Extended solutions, Harmonic maps, Shift-invariant subspaces, Unitons",
author = "Alexandru Aleman and Mart{\'i}n, {Mar{\'i}a J.} and Persson, {Anna Maria} and Martin Svensson",
year = "2019",
month = "12",
day = "1",
doi = "10.1007/s00605-019-01265-x",
language = "English",
volume = "190",
pages = "599--614",
journal = "Monatshefte f{\"u}r Mathematik",
issn = "0026-9255",
publisher = "Springer",
number = "4",

}

Continuous deformations of harmonic maps and their unitons. / Aleman, Alexandru; Martín, María J.; Persson, Anna Maria; Svensson, Martin.

In: Monatshefte fur Mathematik, Vol. 190, No. 4, 01.12.2019, p. 599-614.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Continuous deformations of harmonic maps and their unitons

AU - Aleman, Alexandru

AU - Martín, María J.

AU - Persson, Anna Maria

AU - Svensson, Martin

PY - 2019/12/1

Y1 - 2019/12/1

N2 - It is known that any harmonic map of finite uniton number from a Riemann surface into U (n) can be deformed into a new harmonic map with an associated S1-invariant extended solution. We study this deformation in detail using operator-theoretic methods. In particular, we show that the corresponding unitons are real analytic functions of the deformation parameter, and that the deformation is closely related to the Bruhat decomposition of the corresponding extended solution.

AB - It is known that any harmonic map of finite uniton number from a Riemann surface into U (n) can be deformed into a new harmonic map with an associated S1-invariant extended solution. We study this deformation in detail using operator-theoretic methods. In particular, we show that the corresponding unitons are real analytic functions of the deformation parameter, and that the deformation is closely related to the Bruhat decomposition of the corresponding extended solution.

KW - Blaschke–Potapov products

KW - Bruhat decomposition

KW - Extended solutions

KW - Harmonic maps

KW - Shift-invariant subspaces

KW - Unitons

U2 - 10.1007/s00605-019-01265-x

DO - 10.1007/s00605-019-01265-x

M3 - Journal article

AN - SCOPUS:85060753678

VL - 190

SP - 599

EP - 614

JO - Monatshefte für Mathematik

JF - Monatshefte für Mathematik

SN - 0026-9255

IS - 4

ER -